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How do you find the inverse of #f(x)=e^x-1#?

Answer 1

To find the inverse of ( f(x) = e^x - 1 ), we first swap ( x ) and ( y ) to get ( x = e^y - 1 ). Then, we solve this equation for ( y ) to find the inverse function:

[ x = e^y - 1 ] [ x + 1 = e^y ] [ \ln(x + 1) = y ]

So, the inverse function of ( f(x) = e^x - 1 ) is ( f^{-1}(x) = \ln(x + 1) ).

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Answer 2

Lincoln Anderson

#f^-1(x)=log_e(x+1)#

Firstly, I'll assume you know that if #f(x)=y# then #f^-1(y)=x#

So now, #f(x)=e^x-1# Rearranging the equation, and taking #y=f(x)# we get #y+1=e^x# Applying log of base #e# on both sides #log_e(y+1)=x# Now, given above that #f^-1(y)=x# So this means, #f^-1(y)=log_e(y+1)#

Replacing #y# as #x# you'll get the answer.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.